Relations: Practice Exercises

Here are various Exercises to accompany the section Relations.  Some Exercises are designed to be done with a partner and to be graded by the partner.

  1. Give the indicated, alternative description of each of the following relations:
    1. Give a set of ordered pairs corresponding to the following arrow diagram:

      2. Note: As you can see, it is possible for an arrow diagram to include some items on either side that are not related to anything.

    2. Give a table of at least 5 ordered pairs (x, y) that satisfy the algebraic relation: x + 2y = 21.
    3. Plot the following relation as points in the (x, y)-plane:
      x y
      -3
      -2
      -1
      0
      1
      2
      3      		 2
      0.5
      0
      0.5
      2
      4.5
      8
    4. Compute the reverse of the relation in part c), and display the results as a set of ordered pairs.

    Solution.

  2. For this exercise, you should work with a partner.  You should each follow the instructions to create a practice exercise with four parts, similar to the previous exercise, trade exercises with your partner, solve the exercise your partner makes, then trade back to grade each other's work.
    1. Create your own arrow diagram by drawing in six arrows from the elements on the left to those on the right:

      2. Have your partner give a set of ordered pairs corresponding to your arrow diagram.

    2. Create your own simple, algebraic equation involving x and y.  Have your partner give a table of at least 5 ordered pairs (x, y) that satisfy your equation.
    3. Fill in the following table with six pairs of relatively small numbers:
      x y












      Have your partner plot your relation as points in the (x, y)-plane.

    4. Compute the reverse of the relation in part c), and display the results as a set of ordered pairs.

    Solution.

Go to Introduction to Functions .

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